NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables

Have you ever tried to figure out the number of certain items you can buy within a particular budget? This can be done by using Linear Equations!!! Linear Equations in Two Variables define the relationship between two specific quantities. Being it speed and distance, cost and profit, purchase and sales, and so on. The NCERT Solutions for Class 9 Maths Chapter 4 Linear Equations in Two Variables give step-by-step solutions to all the exercise problems in the Class 9 Maths Book.

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1. Linear Equations in Two Variables Class 9 Questions And Answers PDF Free Download
2. Linear Equations in Two Variables Class 9 Solutions - Important Formulae
3. NCERT Solutions for Class 9 Maths Chapter 4: Exercise Questions
4. Class 9 Maths NCERT Chapter 4: Extra Question
5. Approach to Solve Questions of Linear Equations In Two Variables Class 9
6. Linear Equations In Two Variables Class 9 Solutions - Exercise Wise
7. NCERT Solutions for Class 9 - Subject Wise
8. NCERT Books and NCERT Syllabus

The NCERT solutions for class 9 ensure clarity in understanding and are designed by subject matter experts at Careers360. These study resources are highly reliable and help the students to score maximum marks, as all the questions in the exams are based on the NCERT Books. For additional practice, students can also refer to the NCERT Exemplar Solutions for Class 9 Maths Chapter 4. Apart from this, solutions of Linear Equations in Two Variables class 9 play an integral role, and students find them really helpful. Also, Linear Equations in Two Variables Class 9 NCERT Chapter Notes give the fundamental concepts and important formulas for exam preparation, making it easier for the students to revise.

Linear Equations in Two Variables Class 9 Questions And Answers PDF Free Download

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Linear Equations in Two Variables Class 9 Solutions - Important Formulae

Linear Equations in Two Variables

The equations with two variables are called Linear Equations. The general form of a linear equation in two variables is ax+by=c, where a,b,c are real numbers and $a\ne 0$ and $b\ne 0$.

Solutions of Linear Equations in Two Variables

The linear equations in two variables have infinitely many solutions. Every solution of linear equations in two variables is a point on the equation's graph.

NCERT Solutions for Class 9 Maths Chapter 4: Exercise Questions

Q1 The cost of a notebook is twice the cost of a pen. Write a linear equation in two variables to represent this statement. (Take the cost of a notebook to be Rs x and that of a pen to be Rs y ).

Answer:

Let the cost of a notebook be Rs x and that of a pen be Rs y.

According to the given condition: The cost of a notebook is twice the cost of a pen.

Thus, $x=2y$

$\Rightarrow x-2y=0$

Q2 (i) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $2x+3y=9.3\overline{5}$

Answer:

Given : $2x+3y=9.3\overline{5}$

$\Rightarrow 2x+3y-9.3\overline{5}=0$

Here , a=2, b=3 and c = $-9.3\overline{5}$

Q2 (ii) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $x-\frac{y}{5}-10=0$

Answer:

Given:

$x-\frac{y}{5}-10=0$

$\Rightarrow x-\frac{y}{5}-10=0$

Here,

a=1,

$b=\frac{-1}{5}$

c = -10

Q2 (iii) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $-2x+3y=6$

Answer:

Given :

$-2x+3y=6$

$\Rightarrow -2x+3y-6=0$

Here , a= -2, b=3 and c = -6

Q2 (iv) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $x=3y$

Answer:

Given : $x=3y$

$\Rightarrow x-3y=0$

Here , a= 1, b= -3 and c =0

Q2 (v) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $2x=-5y$

Answer:

Given : $2x=-5y$

$\Rightarrow 2x+5y=0$

Here , a=2, b= 5 and c =0

Q2 (vi) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $3x+2=0$

Answer:

Given : $3x+2=0$

$\Rightarrow 3x+2=0$

Here , a= 3, b=0 and c =2

Q2 (vii) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $y-2=0$

Answer:

Given : $y-2=0$

$\Rightarrow 0.x+y-2=0$

Here , a=0, b= 1 and c = -2

Q2 (viii) Express the following linear equations in the form $ax+by+c=0$ and indicate the values of a, b and c in each case: $5=2x$

Answer:

Given: $5=2x$

$\Rightarrow 2x+0.y-5=0$

Here , a=2, b= 0 and c = -5

Q1 Which one of the following options is true, and why? $y=3x+5$ has

(i) a unique solution,

(ii) only two solutions,

(iii) infinitely many solutions

Answer:

Given : $y=3x+5$

This equation is of a line and a line has infinite points on it and each point is a solution Thus, (iii) infinitely many solutions is the correct option.

Q2 Write four solutions for each of the following equations:

(i) $2x+y=7$ (ii) $\pi x+y=9$ (iii) $x=4y$

Answer:

(i) Given : $2x+y=7$

Putting x=0, we have , $y=7-2\times 0=7$ means $(0,7)$ is a solution.

Putting x=1, we have , $y=7-2\times 1=5$ means $(1,5)$ is a solution.

Putting x=2, we have , $y=7-2\times 2=3$ means $(2,3)$ is a solution.

Putting x=3, we have , $y=7-2\times 3=1$ means $(3,1)$ is a solution.

The four solutions are : $(0,7),(1,5),(2,3),(3,1)$ .

(ii) Given : $\pi x+y=9$

Putting x=0, we have , $y=9-\pi \times 0=9$ means $(0,9)$ is a solution.

Putting x=1, we have , $y=9-\pi \times 1=9-\pi$ means $(1,9-\pi )$ is a solution.

Putting x=2, we have , $y=9-\pi \times 2=9-2\pi$ means $(2,9-2\pi )$ is a solution.

Putting x=3, we have , $y=9-\pi \times 3=9-3\pi$ means $(3,9-3\pi )$ is a solution.

The four solutions are : $(0,9),(1,9-\pi ),(2,9-2\pi ),(3,9-3\pi )$ .

(iii) Given: $x=4y$

Putting x=0, we have , $y=\frac{0}{4}=0$ means $(0,0)$ is a solution.

Putting x=1, we have , $y=\frac{1}{4}$ means $(1,\frac{1}{4})$ is a solution.

Putting x=2, we have , $y=\frac{2}{4}=\frac{1}{2}$ means $(2,\frac{1}{2})$ is a solution.

Putting x=3, we have , $y=\frac{3}{4}$ means $(3,\frac{3}{4})$ is a solution.

The four solutions are : $(0,0)$ , $(1,\frac{1}{4})$ , $(2,\frac{1}{2})$ and $(3,\frac{3}{4})$ .

Q3 (i) Check which of the following are solutions of the equation $x-2y=4$ and which are not: ((0,2)

Answer:

(i) Given : $x-2y=4$

Putting $(0,2)$ ,

we have , $x-2y=0-2(2)=-4\ne 4$

Therefore, $(0,2)$ is not a solution of $x-2y=4$ .

Q3 (ii) Check which of the following are solutions of the equation $x-2y=4$ and which are not: (2,0)

Answer:

Given : $x-2y=4$

Putting (2,0),

we have , $x-2y=2-2(0)=2\ne 4$

Therefore, (2,0) is not a solution of $x-2y=4$.

Q3 (iii) Check which of the following are solutions of the equation $x-2y=4$ and which are not: (4,0)

Answer:

Given : $x-2y=4$

Putting (4,0),

we have , $x-2y=4-2(0)=4=4$

Therefore, (4,0) is a solution of $x-2y=4$.

Q3 (iv) Check which of the following are solutions of the equation $x-2y=4$ and which are not: $(\sqrt{2},4\sqrt{2})$

Answer:

Given : $x-2y=4$

Putting $(\sqrt{2},4\sqrt{2})$ ,

we have , $x-2y=\sqrt{2}-2(4\sqrt{2})=\sqrt{2}-8\sqrt{2}=-7\sqrt{2}\ne 4$

Therefore, $(\sqrt{2},4\sqrt{2})$ is not a solution of $x-2y=4$ .

Q3 (v) Check which of the following are solutions of the equation $x-2y=4$ and which are not: (1,1)

Answer:

Given : $x-2y=4$

Putting (1,1),

we have , $x-2y=1-2(1)=-1\ne 4$

Therefore, (1,1) is not a solution of $x-2y=4$ .

Q4 Find the value of k , if $x=2$ , $y=1$ is a solution of the equation $2x+3y=k$ .

Answer:

Given : $2x+3y=k$

Putting (2,1),

we have , $k=2x+3y=2(2)+3(1)=4+3=7$

Therefore, k=7 for $2x+3y=k$ putting x=2 and y=1.

Class 9 Maths NCERT Chapter 4: Extra Question

Question: Find the value of $y$ in the equation $2x+3y=12$ when $x=3$.

Answer:

First, substitute $x=3$ into the equation:

We get, $2(3)+3y=12\Rightarrow 6+3y=12$

$3y=12-6=6\Rightarrow y=\frac{6}{3}=2$

Thus, the value of $y$ is 2.

Approach to Solve Questions of Linear Equations In Two Variables Class 9

1. Understand the standard form: A linear equation consisting of two variables uses the form of $ax+by+c=0$ for all its components to be real numbers and also $a,b/neq0$.

2. Know that each solution is a pair of values: The equation accepts ordered pairs (x,y) which solve the equation during substitution.

3. Use substitution to find solutions: Executing different x (or y) value substitutions helps determine corresponding values of the opposite variable.

4. Create tables of values: Make value tables that contain 3–5 solutions to reveal the relationship between the x and y variables.

5. Graph the solutions: Draw the pairs of solution points on a Cartesian coordinate system to see that they form a straight line.

6. Interpret the meaning of infinite solutions: The system of a linear equation that includes two variables can have numerous solutions defined through points which exist on the same straight line.

Linear Equations In Two Variables Class 9 Solutions - Exercise Wise

Interested students can practice the Class 9 Maths Chapter 4 exercise problems using the links given below. The NCERT Solutions for Linear Equations in Two Variables help simplify the process of finding solutions using substitution and plotting.

• NCERT Solutions for Class 9 Maths Exercise 4.1
• NCERT Solutions for Class 9 Maths Exercise 4.2

NCERT Solutions for Class 9 Maths Chapter Wise

NCERT Solutions for Class 9 - Subject Wise

Students can also refer to the NCERT Subject Wise Solutions for Class 9.

• NCERT Solutions for Class 9 Maths
• NCERT Solutions for Class 9 Science

NCERT Books and NCERT Syllabus

We at Careers360 provide the links for Class 9 NCERT Books and NCERT Syllabus, making it easily accessible to the students. Below are the links for other study resources of NCERT Class 9.

• NCERT Books Class 9 Maths
• NCERT Syllabus Class 9 Maths
• NCERT Books Class 9
• NCERT Syllabus Class 9